FED UP! Cornerback Brandon Carr (right), who signed with Dallas as a free agent over the offseason and has never played against the Giants as a member of the Cowboys, says many in the locker room are tired of hearing about Big Blue’s titles and wonder when it’ll be their time. Photo: Reuters

IRVING, Texas — The Cowboys have Big Blue on the brain, and they’re not afraid to admit it.

Dallas has become so obsessed with the Giants, in fact, that even a player who has been with the team all of about 10 minutes is giving Big Blue bulletin-board material.

Brandon Carr, Dallas’ prized free-agent addition in the offseason, tried to stoke what has become a very one-sided rivalry yesterday by saying his teammates have a case of Giants Championship Fatigue heading into tomorrow night’s opener at MetLife Stadium.

“[The Giants] have had great success, winning two Super Bowls in five years, and I think guys are kind of getting tired of seeing that,” the veteran cornerback said. “Now it’s to the point guys are getting fed up. It’s pretty much the attitude, ‘When is it going to be our time?’ ”

Carr isn’t the only Cowboys coach, player or — most famously — owner that has seemed more than a little obsessed with the Giants since Tom Coughlin’s team ended Dallas’ season eight months ago with a Week 17 drubbing at the Meadowlands.

Jerry Jones certainly left no doubt in late July which team is on his mind when he invited the crowd at the team’s training-camp kickoff party in Oxnard, Calif., to “come to Cowboys Stadium and watch us beat the Giants’ asses.”

That opportunity won’t come until Oct. 28, when the Giants visit Arlington for an NFC East divisional return match, but Jones’ team has done precious little of beating Big Blue’s behinds in recent years.

The Cowboys are just 2-7 against the Giants since January 2008, including a painful, final-month sweep at the hands of Coughlin’s club last year that cemented Dallas’ second consecutive year without a playoff trip.

Cowboys defensive coordinator Rob Ryan, Rex’s less-svelte brother, admitted yesterday he’s still smarting over the two losses to the Giants last season, particularly the 31-14 rout on the final day that decided the division.

“Hell, it knocked us out of the playoffs — so I took offense to it,” Ryan said. “Did it ruin my offseason? No. They were the best team in the league and won the Super Bowl. But do I plan to do something about it? Yeah.”

Cowboys quarterback Tony Romo usually tries to avoid any and all touchy subjects in his weekly sessions with the media, but even he couldn’t resist making it known how eager he is for revenge.

“I got pumped up the second I found out our schedule and heard they were our first game,” Romo said.

For his part, Jones toned down the anti-Giants rhetoric dramatically in the days leading up to this week’s game. Vows to beat their butts were replaced by flowery compliments.

“It’s a great opportunity for us,” Jones said Sunday. “Everybody here has all the appreciation in the world for the quality of that [Giants] franchise. To have success up there this week would be very meaningful. It’s going to be a highly visible game against the world champions.”

Jones also claimed he was “very pleased” when he found out the NFL had scheduled the Cowboys to open against the Giants, even if it meant a grueling road game for his team right off the bat.

“It’s going to be quite a challenge, but one we’re looking forward to very much,” the Dallas boss said.

Carr can count his time in the Cowboys’ locker room in terms of days rather than years, but he said he senses his new teammates are both juiced and confident about their chances of knocking off the defending Lombardi Trophy winners.

“I can feel the anticipation,” Carr said. “I’ve been hearing about [the Giants] for a long time now, and we’re all just ready to go out there and play them. We love getting the first crack at the defending Super Bowl champions.”